Nuprl Lemma : alg_div_wf
∀A:Type. ∀a:algebra_sig{i:l}(A). (a.div ∈ a.car ⟶ a.car ⟶ (a.car?))
Proof
Definitions occuring in Statement :
alg_div: a.div,
alg_car: a.car,
algebra_sig: algebra_sig{i:l}(A),
all: ∀x:A. B[x],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
algebra_sig: algebra_sig{i:l}(A),
alg_div: a.div,
alg_car: a.car,
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
algebra_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesisEquality,
hypothesis,
lemma_by_obid,
dependent_functionElimination,
universeEquality
Latex:
\mforall{}A:Type. \mforall{}a:algebra\_sig\{i:l\}(A). (a.div \mmember{} a.car {}\mrightarrow{} a.car {}\mrightarrow{} (a.car?))
Date html generated:
2016_05_16-AM-07_26_10
Last ObjectModification:
2015_12_28-PM-05_08_10
Theory : algebras_1
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