Nuprl Lemma : qadd_functionality_wrt_qless
∀[a,b,c,d:ℚ]. (a + c < b + d) supposing ((c ≤ d) and a < b)
Proof
Definitions occuring in Statement :
qle: r ≤ s,
qless: r < s,
qadd: r + s,
rationals: ℚ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
qless_transitivity_1_qorder,
iff_weakening_equal,
qadd_com,
true_wf,
squash_wf,
grp_op_preserves_lt_qorder,
grp_op_preserves_le_qorder,
rationals_wf,
qless_wf,
qle_wf,
qadd_wf,
qless_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination
Latex:
\mforall{}[a,b,c,d:\mBbbQ{}]. (a + c < b + d) supposing ((c \mleq{} d) and a < b)
Date html generated:
2016_05_15-PM-11_00_02
Last ObjectModification:
2016_01_16-PM-09_31_06
Theory : rationals
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