Nuprl Lemma : provisional-monad_wf
provisional-monad{i:l}() ∈ Monad'
Proof
Definitions occuring in Statement :
provisional-monad: provisional-monad{i:l}(),
monad: Monad,
member: t ∈ T
Definitions unfolded in proof :
provisional-monad: provisional-monad{i:l}(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
allowed: allowed(x),
provision: provision(ok; v),
bind-provision: bind-provision(x;t.f[t]),
allow: allow(x),
pi1: fst(t),
pi2: snd(t),
cand: A c∧ B,
true: True,
squash: ↓T,
rev_implies: P ⇐ Q
Lemmas referenced :
mk_monad_wf,
provisional-type_wf,
istype-universe,
provision_wf,
true_wf,
squash_wf,
bind-provision_wf,
provisional-type-equality,
squash-implies-usquash,
usquash_wf,
allowed_wf,
usquash-elim,
sq_stable__and,
sq_stable_usquash,
sq_stable__allowed,
sq_stable_from_decidable,
decidable__true,
allow_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality_alt,
hypothesisEquality,
hypothesis,
universeEquality,
sqequalRule,
isect_memberEquality_alt,
universeIsType,
applyEquality,
functionIsType,
inhabitedIsType,
independent_isectElimination,
isect_memberFormation_alt,
lambdaFormation_alt,
equalitySymmetry,
independent_pairFormation,
productEquality,
independent_functionElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
because_Cache,
productElimination,
dependent_functionElimination,
axiomEquality,
functionIsTypeImplies,
isectIsTypeImplies
Latex:
provisional-monad\{i:l\}() \mmember{} Monad'
Date html generated:
2020_05_20-AM-08_01_11
Last ObjectModification:
2020_05_17-PM-07_57_29
Theory : monads
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