Nuprl Lemma : all-nsub2
∀[P:ℕ2 ⟶ ℙ]. (∀x:ℕ2. P[x] ⇐⇒ P[0] ∧ P[1])
Proof
Definitions occuring in Statement :
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
less_than: a < b,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
int_seg_properties,
int_subtype_base,
subtype_base_sq,
decidable__equal_int,
lelt_wf,
false_wf,
int_seg_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesisEquality,
productEquality,
dependent_set_memberEquality,
introduction,
imageMemberEquality,
baseClosed,
universeEquality,
because_Cache,
functionEquality,
cumulativity,
dependent_functionElimination,
setElimination,
rename,
unionElimination,
instantiate,
intEquality,
independent_isectElimination,
independent_functionElimination,
productElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll
Latex:
\mforall{}[P:\mBbbN{}2 {}\mrightarrow{} \mBbbP{}]. (\mforall{}x:\mBbbN{}2. P[x] \mLeftarrow{}{}\mRightarrow{} P[0] \mwedge{} P[1])
Date html generated:
2016_05_15-PM-03_27_26
Last ObjectModification:
2016_01_16-AM-10_48_27
Theory : general
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