Nuprl Lemma : sq_stable__eqfun_p
∀[T:Type]. ∀[eq:T ⟶ T ⟶ 𝔹]. SqStable(IsEqFun(T;eq))
Proof
Definitions occuring in Statement :
eqfun_p: IsEqFun(T;eq),
bool: 𝔹,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
eqfun_p: IsEqFun(T;eq),
uall: ∀[x:A]. B[x],
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
infix_ap: x f y,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T
Lemmas referenced :
assert_wf,
assert_witness,
equal_wf,
squash_wf,
uall_wf,
uiff_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
isect_memberEquality,
isectElimination,
productElimination,
independent_pairEquality,
axiomEquality,
hypothesis,
extract_by_obid,
applyEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
Error :functionIsType,
Error :universeIsType,
Error :inhabitedIsType,
because_Cache,
functionEquality,
universeEquality,
lemma_by_obid,
imageElimination,
lambdaFormation
Latex:
\mforall{}[T:Type]. \mforall{}[eq:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbB{}]. SqStable(IsEqFun(T;eq))
Date html generated:
2019_06_20-PM-00_29_13
Last ObjectModification:
2018_09_26-PM-00_00_57
Theory : rel_1
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