Nuprl Lemma : subst-exc-basecase
∀[v:Top]. ∀[e:Atom2]. (subst-exc(e;exception(e; v)) ~ ⊥)
Proof
Definitions occuring in Statement :
bottom: ⊥,
subst-exc: subst-exc(e;t),
atom: Atom$n,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subst-exc: subst-exc(e;t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q
Lemmas referenced :
top_wf,
eq_atom2_self,
btrue_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom2,
eqff_to_assert,
eq_atom_wf2,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
iff_transitivity,
assert_wf,
bnot_wf,
not_wf,
equal-wf-base,
atom2_subtype_base,
iff_weakening_uiff,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
sqequalAxiom,
atomnEquality,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
extract_by_obid,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
atomn_eqReduceTrueSq,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
applyEquality,
independent_pairFormation,
impliesFunctionality
Latex:
\mforall{}[v:Top]. \mforall{}[e:Atom2]. (subst-exc(e;exception(e; v)) \msim{} \mbot{})
Date html generated:
2017_04_14-AM-07_15_58
Last ObjectModification:
2017_02_27-PM-02_51_15
Theory : call!by!value_1
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