Nuprl Lemma : quot-implies-squash
∀P:ℙ. (⇃(P) ⇒ (↓P))
Proof
Definitions occuring in Statement :
quotient: x,y:A//B[x; y],
prop: ℙ,
all: ∀x:A. B[x],
squash: ↓T,
implies: P ⇒ Q,
true: True
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
true: True,
cand: A c∧ B,
squash: ↓T,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
istype-universe,
true_wf,
squash_wf,
member_wf,
quotient_wf,
equiv_rel_true
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
promote_hyp,
Error :universeIsType,
natural_numberEquality,
independent_pairFormation,
sqequalRule,
imageMemberEquality,
baseClosed,
dependent_functionElimination,
pointwiseFunctionality,
pertypeElimination,
productElimination,
independent_functionElimination,
Error :productIsType,
Error :equalityIsType4,
equalityTransitivity,
equalitySymmetry,
imageElimination,
Error :lambdaEquality_alt,
Error :inhabitedIsType,
independent_isectElimination,
universeEquality
Latex:
\mforall{}P:\mBbbP{}. (\00D9(P) {}\mRightarrow{} (\mdownarrow{}P))
Date html generated:
2019_06_20-PM-02_54_36
Last ObjectModification:
2018_10_05-PM-10_38_33
Theory : continuity
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