Nuprl Lemma : FormSafe1'-iff-FormSafe1''
∀C:Type. ∀f:Form(C). ∀vs:Atom List. (FormSafe1'(f) vs ⇐⇒ FormSafe1''(f) vs)
Proof
Definitions occuring in Statement :
FormSafe1'': FormSafe1''(f),
FormSafe1': FormSafe1'(f),
Form: Form(C),
list: T List,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
apply: f a,
atom: Atom,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
FormSafe1'': FormSafe1''(f),
FormSafe1': FormSafe1'(f),
FormVar: Vname,
Form_ind: Form_ind,
iff: P ⇐⇒ Q,
and: P ∧ Q,
false: False,
prop: ℙ,
rev_implies: P ⇐ Q,
FormConst: Const(value),
FormSet: {var | phi},
FormEqual: left = right,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
or: P ∨ Q,
FormMember: element ∈ set,
FormAnd: left ∧ right),
guard: {T},
FormOr: left ∨ right,
FormNot: ¬(body),
FormAll: ∀var. body,
FormExists: ∃var. body,
not: ¬A,
exists: ∃x:A. B[x],
let: let,
cand: A c∧ B,
set-equal: set-equal(T;x;y),
l_subset: l_subset(T;as;bs),
decidable: Dec(P)
Lemmas referenced :
Form-induction,
all_wf,
list_wf,
iff_wf,
FormSafe1'_wf,
FormSafe1''_wf,
Form_wf,
false_wf,
or_wf,
assert_wf,
null_wf3,
subtype_rel_list,
top_wf,
exists_wf,
set-equal_wf,
cons_wf,
nil_wf,
FormVar?_wf,
equal-wf-T-base,
FormVar-name_wf,
atom_subtype_base,
not_wf,
l_member_wf,
FormFvs_wf,
l_subset_wf,
list-diff_wf,
atom-deq_wf,
let_wf,
FormSafe-iff-FormSafe1',
FormSafe1-Fvs-subset,
decidable__l_member,
decidable__atom_equal,
member-list-diff,
FormSafe1_functionality,
FormSafe1_wf,
equal_wf,
and_wf,
l_subset_refl
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
atomEquality,
hypothesis,
applyEquality,
cumulativity,
independent_functionElimination,
independent_pairFormation,
voidElimination,
because_Cache,
independent_isectElimination,
isect_memberEquality,
voidEquality,
productEquality,
unionElimination,
inlFormation,
inrFormation,
instantiate,
universeEquality,
productElimination,
dependent_functionElimination,
promote_hyp,
addLevel,
impliesFunctionality,
functionEquality,
equalityTransitivity,
equalitySymmetry,
hyp_replacement,
dependent_set_memberEquality,
applyLambdaEquality,
setElimination,
rename,
dependent_pairFormation
Latex:
\mforall{}C:Type. \mforall{}f:Form(C). \mforall{}vs:Atom List. (FormSafe1'(f) vs \mLeftarrow{}{}\mRightarrow{} FormSafe1''(f) vs)
Date html generated:
2018_05_21-PM-11_30_01
Last ObjectModification:
2017_10_12-PM-03_54_12
Theory : PZF
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